Generation interval contraction and epidemic data analysis

The generation interval is the time between the infection time of an infected person and the infection time of his or her infector. Probability density functions for generation intervals have been an important input for epidemic models and epidemic data analysis. In this paper, we specify a general stochastic SIR epidemic model and prove that the mean generation interval decreases when susceptible persons are at risk of infectious contact from multiple sources. The intuition behind this is that when a susceptible person has multiple potential infectors, there is a ``race'' to infect him or her in which only the first infectious contact leads to infection. In an epidemic, the mean generation interval contracts as the prevalence of infection increases. We call this global competition among potential infectors. When there is rapid transmission within clusters of contacts, generation interval contraction can be caused by a high local prevalence of infection even when the global prevalence is low. We call this local competition among potential infectors. Using simulations, we illustrate both types of competition. Finally, we show that hazards of infectious contact can be used instead of generation intervals to estimate the time course of the effective reproductive number in an epidemic. This approach leads naturally to partial likelihoods for epidemic data that are very similar to those that arise in survival analysis, opening a promising avenue of methodological research in infectious disease epidemiology.Comment: 20 pages, 5 figures; to appear in Mathematical Bioscience

A Modified Janus Cassette (Sweet Janus) to Improve Allelic Replacement Efficiency by High-Stringency Negative Selection in Streptococcus pneumoniae

The Janus cassette permits marker-free allelic replacement or knockout in streptomycin-resistant Streptococcus pneumoniae (pneumococcus) through sequential positive and negative selection. Spontaneous revertants of Janus can lead to high level of false-positives during negative selection, which necessitate a time-consuming post-selection screening process. We hypothesized that an additional counter-selectable marker in Janus would decrease the revertant frequency and reduce false-positives, since simultaneous reversion of both counter-selectable makers is much less likely. Here we report a modified cassette, Sweet Janus (SJ), in which the sacB gene from Bacillus subtilis conferring sucrose sensitivity is added to Janus. By using streptomycin and sucrose simultaneously as selective agents, the frequency of SJ double revertants was about 105-fold lower than the frequency of Janus revertants. Accordingly, the frequency of false-positives in the SJ-mediated negative selection was about 100-fold lower than what was seen for Janus. Thus, SJ enhances negative selection stringency and can accelerate allelic replacement in pneumococcus, especially when transformation frequency is low due to strain background or suboptimal transformation conditions. Results also suggested the sacB gene alone can function as a counter-selectable marker in the Gram-positive pneumococcus, which will have the advantage of not requiring a streptomycin-resistant strain for allelic replacement

Monitoring the fitness of antiviral-resistant influenza strains during an epidemic: a mathematical modelling study

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Managing and reducing uncertainty in an emerging influenza pandemic

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Optimizing the Dose of Pre-Pandemic Influenza Vaccines to Reduce the Infection Attack Rate

Steven Riley and colleagues examine the potential benefits of "stretching" a limited supply of vaccine and suggest that substantial reductions in the attack rate are possible if vaccines are given to more people at lower doses

Impact of Interdisciplinary Undergraduate Research in Mathematics and Biology on the Development of a New Course Integrating Five STEM Disciplines

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a course for first-year students that integrates the material in the first course of the major in each of biology, chemistry, mathematics, computer science, and physics

Prediction of serotypes causing invasive pneumococcal disease in unvaccinated and vaccinated populations.

INTRODUCTION: Before the introduction of the heptavalent pneumococcal conjugate vaccine (Prevnar-7), the relative prevalence of serotypes of Streptococcus pneumoniae was fairly stable worldwide. We sought to develop a statistical tool to predict the relative frequency of different serotypes among disease isolates in the pre- and post-Prevnar-7 eras using the limited amount of data that is widely available. METHODS: We initially used pre-Prevnar-7 carriage prevalence and estimates of invasiveness derived from case-fatality data as predictors for the relative abundance of serotypes causing invasive pneumococcal disease during the pre- and post-Prevnar-7 eras, using negative binomial regression. We fit the model to pre-Prevnar-7 invasive pneumococcal disease data from England and Wales and used these data to (1) evaluate the performance of the model using several datasets and (2) evaluate the utility of the country-specific carriage data. We then fit an alternative model that used polysaccharide structure, a correlate of prevalence that does not require country-specific information and could be useful in determining the postvaccine population structure, as a predictor. RESULTS: Predictions from the initial model fit data from several pediatric populations in the pre-Prevnar-7 era. After the introduction of Prevnar-7, the model still had a good negative predictive value, though substantial unexplained variation remained. The alternative model had a good negative predictive value but poor positive predictive value. Both models demonstrate that the pneumococcal population follows a somewhat predictable pattern even after vaccination. CONCLUSIONS: This approach provides a preliminary framework to evaluate the potential patterns and impact of serotypes causing invasive pneumococcal disease

Mutational pathway determines whether drug gradients accelerate evolution of drug-resistant cells

Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anti-cancer drugs. We use a statistical physics model to study the evolution of a population of malignant cells exposed to drug gradients, where drug resistance emerges via a mutational pathway involving multiple mutations. We show that a non-uniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients. These predictions can be verified experimentally, and may help to improve strategies for combatting the emergence of resistance.Comment: 6 pages, 3 figures, final version before acceptance to Phys. Rev. Letters. P.G and B.W contributed equally to this wor

Limited available evidence supports theoretical predictions of reduced vaccine efficacy at higher exposure dose

Understanding the causes of vaccine failure is important for predicting disease dynamics in vaccinated populations and planning disease interventions. Pathogen exposure dose and heterogeneity in host susceptibility have both been implicated as important factors that may reduce overall vaccine efficacy and cause vaccine failure. Here, we explore the effect of pathogen dose and heterogeneity in host susceptibility in reducing efficacy of vaccines. Using simulation-based methods, we find that increases in pathogen exposure dose decrease vaccine efficacy, but this effect is modified by heterogeneity in host susceptibility. In populations where the mode of vaccine action is highly polarized, vaccine efficacy decreases more slowly with exposure dose than in populations with less variable protection. We compared these theoretical results to empirical estimates from a systematic literature review of vaccines tested over multiple exposure doses. We found that few studies (nine of 5,389) tested vaccine protection against infection over multiple pathogen challenge doses, with seven studies demonstrating a decrease in vaccine efficacy with increasing exposure dose. Our research demonstrates that pathogen dose has potential to be an important determinant of vaccine failure, although the limited empirical data highlight a need for additional studies to test theoretical predictions on the plausibility of reduced host susceptibility and high pathogen dose as mechanisms responsible for reduced vaccine efficacy in high transmission settings